A minimizing property of the Sphere?
$begingroup$
From the wiki “Sphere” entry:
“The sphere has the smallest surface area of all surfaces that enclose
a given volume, and it encloses the largest volume among all closed
surfaces with a given surface area.”
Does this statement, particularly the latter part, imply that of all possible configurations of the same volume V, the sphere also maximizes the minimum-distance from any point inside the sphere to the sphere’s surface?
(If so, I’m assuming this would only apply to genus-0 objects.)
maxima-minima average spheres minimal-surfaces
asked Dec 28 '18 at 5:03
user86742user86742
63
$endgroup$
add a comment |
$begingroup$
From the wiki “Sphere” entry:
“The sphere has the smallest surface area of all surfaces that enclose
a given volume, and it encloses the largest volume among all closed
surfaces with a given surface area.”
Does this statement, particularly the latter part, imply that of all possible configurations of the same volume V, the sphere also maximizes the minimum-distance from any point inside the sphere to the sphere’s surface?
(If so, I’m assuming this would only apply to genus-0 objects.)
maxima-minima average spheres minimal-surfaces
asked Dec 28 '18 at 5:03
user86742user86742
63
$endgroup$
add a comment |
$begingroup$
From the wiki “Sphere” entry:
“The sphere has the smallest surface area of all surfaces that enclose
a given volume, and it encloses the largest volume among all closed
surfaces with a given surface area.”
Does this statement, particularly the latter part, imply that of all possible configurations of the same volume V, the sphere also maximizes the minimum-distance from any point inside the sphere to the sphere’s surface?
(If so, I’m assuming this would only apply to genus-0 objects.)
maxima-minima average spheres minimal-surfaces
asked Dec 28 '18 at 5:03
user86742user86742
63
$endgroup$
From the wiki “Sphere” entry:
“The sphere has the smallest surface area of all surfaces that enclose
a given volume, and it encloses the largest volume among all closed
surfaces with a given surface area.”
Does this statement, particularly the latter part, imply that of all possible configurations of the same volume V, the sphere also maximizes the minimum-distance from any point inside the sphere to the sphere’s surface?
(If so, I’m assuming this would only apply to genus-0 objects.)
maxima-minima average spheres minimal-surfaces
maxima-minima average spheres minimal-surfaces
asked Dec 28 '18 at 5:03
user86742user86742
63
asked Dec 28 '18 at 5:03
user86742user86742
63
asked Dec 28 '18 at 5:03
user86742user86742
63
asked Dec 28 '18 at 5:03
user86742user86742
63
asked Dec 28 '18 at 5:03
user86742user86742
63
63
add a comment |
add a comment |
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